# Kinetic Energy Formula definition explanation

1. Apr 10, 2013

### Selina94

1. The problem statement, all variables and given/known data
I'm trying to understand how this equation was came together, mainly, I hardly understand why velocity is squared, and why there's the constant of '1/2'.

2. Relevant equations
In classical mechanics, the kinetic energy of a point object (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body depends on the mass of the body as well as its speed. The kinetic energy is equal to the mass multiplied by the square of the speed, multiplied by the constant 1/2. In formula form:

2. Apr 10, 2013

### hms.tech

Work done on an object and one of the equation of motion for constant acceleration :

V^2 - U^2 = 2AD (A= acceleration vector)(D= Displacement vector)(the rest is self explanatory)
W=F.D

3. Apr 10, 2013

### vela

Staff Emeritus
Integrate the righthand side of
$$\int \vec{F}\cdot d\vec{r} = \int m\vec{a}\cdot d\vec{r}$$ using the chain rule to write $a_i = \frac{d v_i}{dt} = \frac{dv_i}{dx_i}\frac{dx_i}{dt}$.